Yep. Bottles should have a small amount of air in the headspace to dampen pressure changes as the liquid expands and contracts with temperature. With no headspace at all, the pressure changes could be rather extreme.I wouldnt fill nic to brim 1/2 inch 12.5 mm of the top is enough.
If you're really OCD, you can displace that air with an inert gas. Vendors who do this will typically use argon. If you're rebottling yourself, cans of wine preservative gas mixture (primarily nitrogen and CO2) are readily available. The idea is to minimize the amount of oxygen in the bottle when it's sealed up. However, Kurt did some math a while back that seemed to show the benefits of doing this would be marginal at best, at least if the headspace is kept small (a few CCs).